Topology optimization is a mathematical method used to determine the optimal design of a structure to achieve desirable functional performance. Traditional single-material topology optimization can be extended to include multiple materials, offering greater design freedom, and the potential for superior layouts. Additive manufacturing technologies have become powerful tools to build up such multi-material solutions. However, inherent limitations in these processes must be considered in the optimal design. One significant challenge in additive manufacturing is the trapping of either unmelted or non-solidified powder, or in some cases, support structures in enclosed voids. This study investigates a gradient-based 3D bi-material topology optimization method that considers not only the volume fraction of each material and total mass constraints but also an additional virtual temperature constraint to avoid enclosed voids. To this end, the virtual temperature method is extended to identify and mitigate enclosed voids in bi-material structures. An efficient and straightforward technique is proposed for interpolating the elemental virtual heat conduction matrix and the elemental thermal load. Additionally, a discrete material optimization approach is employed to interpolate the elemental stiffness matrix. The problem formulation and sensitivities are thoroughly discussed. The method of moving asymptotes is used to update the design variables, which are the element densities of each material. 3D numerical results are presented to demonstrate the capability and feasibility of the proposed implementation, thereby providing superior performing designs with minimal impact on the structural performance.

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